TY - JOUR

T1 - On an alternative approach for simulating chemically induced crack pattern evolutions in a single crystal

AU - Predan, Jozef

AU - Kegl, M.

AU - Abart, Rainer

AU - Fischer, Franz-Dieter

AU - Rammerstorfer, Franz G.

PY - 2020/10/1

Y1 - 2020/10/1

N2 - The evolution of essentially periodic crack patterns appears in many natural and technical processes. For example, typical cases of periodic crack patterns are known from drying soils, from the formation of basalt columns, from high temperature loaded ceramics, from fissure formation in coke, and from drying protein solution drops. The appearance of more or less periodic crack patterns is the result of cascades of bifurcation-instabilities of the propagation process. There exist established, mathematically rigorous criteria for the bifurcation of the crack growth process of two initially equally long parallel cracks (Nemat-Nasser et al., 1978; Bazant et al., 1979). These criteria require the determination of the mutual influence of the neighboring cracks on their growth by calculation of partial derivatives. If discretization methods are used for simulating such a growth process, the calculation of these partial derivatives may become very sensitive with respect to the density of the spatial discretization. This is especially true if strong gradients of a crack driving eigenstress field appear as, for instance, in chemical diffusion processes. In the present paper, an alternative approach is introduced, which circumvents estimations of partial derivatives and, in addition, provides a more realistic picture of the generation of crack patterns. This approach is inspired by a computationally efficient method for investigating the buckling and post-buckling behavior in structural mechanics by introducing small imperfections. As a typical example, in which the approach introduced here is especially beneficial, the simulation of self-organized crack pattern evolution in alkali feldspar, a very common brittle crystal, is presented. There, the cracks are driven by eigenstrains caused by cation exchange between the crystal and a salt melt. Comparisons between the character of the pattern formation in the simulation and in experiments show excellent agreement. Furthermore, by combining simulations and experiments the J
c-value can be determined at considerably high accuracy.

AB - The evolution of essentially periodic crack patterns appears in many natural and technical processes. For example, typical cases of periodic crack patterns are known from drying soils, from the formation of basalt columns, from high temperature loaded ceramics, from fissure formation in coke, and from drying protein solution drops. The appearance of more or less periodic crack patterns is the result of cascades of bifurcation-instabilities of the propagation process. There exist established, mathematically rigorous criteria for the bifurcation of the crack growth process of two initially equally long parallel cracks (Nemat-Nasser et al., 1978; Bazant et al., 1979). These criteria require the determination of the mutual influence of the neighboring cracks on their growth by calculation of partial derivatives. If discretization methods are used for simulating such a growth process, the calculation of these partial derivatives may become very sensitive with respect to the density of the spatial discretization. This is especially true if strong gradients of a crack driving eigenstress field appear as, for instance, in chemical diffusion processes. In the present paper, an alternative approach is introduced, which circumvents estimations of partial derivatives and, in addition, provides a more realistic picture of the generation of crack patterns. This approach is inspired by a computationally efficient method for investigating the buckling and post-buckling behavior in structural mechanics by introducing small imperfections. As a typical example, in which the approach introduced here is especially beneficial, the simulation of self-organized crack pattern evolution in alkali feldspar, a very common brittle crystal, is presented. There, the cracks are driven by eigenstrains caused by cation exchange between the crystal and a salt melt. Comparisons between the character of the pattern formation in the simulation and in experiments show excellent agreement. Furthermore, by combining simulations and experiments the J
c-value can be determined at considerably high accuracy.

KW - Bifurcation

KW - Crack arrest

KW - Imperfections

KW - Stability

UR - http://www.scopus.com/inward/record.url?scp=85088099262&partnerID=8YFLogxK

U2 - 10.1016/j.ijsolstr.2020.06.006

DO - 10.1016/j.ijsolstr.2020.06.006

M3 - Article

SN - 0020-7683

VL - 202

SP - 575

EP - 586

JO - International journal of solids and structures

JF - International journal of solids and structures

M1 - 202

ER -